Oth large and small-sized social structures. The differences are greater when the relative performance of the innovation on the status quo is not very large. Nevertheless, despite this higher probability of success regarding other topologies, hierarchy is the structure that requires more time to reach a favorable consensus. As is well known, time has a cost (referred to in economy as opportunity cost), established by the profitability of its alternative use. On the other hand, the hierarchical appears as a very stable structure, showing a lower sensitivity to changes in the parameters of the model. ER and BA structures give a very low probability of adoption for small innovation performance with respect to the status quo and are especially sensitive to changes in the rate of learning and social pressure. However, they present an remarkable advantage in the time needed to achieve favorable consensus as compared with a hierarchical graph.The modelLet I = 1, 2, . . ., N be the set of nodes in a social system structure: each node represents an individual or a team of several individuals under a common working PX105684 mechanism of action method (whether subject to discipline or reached by consensus). For each node j 2 I there is, at least, another node i 2 I,i 6?j to which it is connected; the graph of relationships is specified by a (N ?N) symmetric adjacency matrix A defined as Aij = 1 whenever i is directly Grazoprevir site connected to j in the social structure, or Aij = 0 otherwise. We define the influence set of node j as the collection of nodes that are directly connected to it: Hj = i 2 IjAij = 1. In the same way, the degree kj of node j is the number of PN nodes directly connected to it: kj ?card j ??i? Aij . Each node i 2 I has knowledge of each working method. Let Rit be the performance of node i at time t provided by the conventional method (status quo) and, in the same way, let R be t the node i’s performance provided by the new method (innovation). In addition, each node i is characterized by a variable si (the strategy) that takes the value sit ?1 if the node i supports the innovation at time t, or sit ?0 otherwise. Let ait be the number of nodes connected to i that support the innovation at time t, and let bit be the number of i’s neighbors that support the status quo: ait ?N X j? N X j?sjt Aij : ??j1 ?sjt jAij ?ki ?aitbit?Given two nodes (i, j) mutually connected, i having adopted the innovation and j having not (i.e., sit ?1; sjt ?0), we establish that they can interact with each other by exchanging knowledge (and exchanging methods) only if the performance difference between the two nodes is contained in an interval : j R ?Rjt j< ; t ??resulting in mutual learning. When condition 2 is satisfied, we define the link (i, j) as feasible. This threshold introduces a condition for mutual benefit: while high values of allow altruism (i.e., people with high performance help people with very low performance without expecting anything in return), low values of only allow win-win relationships.PLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,3 /The Role of the Organization Structure in the Diffusion of InnovationsInitial conditionsThe system begins with a number of randomly distributed nodes (the initial adopters) that adopt the innovation from the first moment t = 0, while the other nodes are supporters of the status quo. The performance provided by the status quo is randomly distributed between the nodes according to a gaussian distribution centered in R = 1 with.Oth large and small-sized social structures. The differences are greater when the relative performance of the innovation on the status quo is not very large. Nevertheless, despite this higher probability of success regarding other topologies, hierarchy is the structure that requires more time to reach a favorable consensus. As is well known, time has a cost (referred to in economy as opportunity cost), established by the profitability of its alternative use. On the other hand, the hierarchical appears as a very stable structure, showing a lower sensitivity to changes in the parameters of the model. ER and BA structures give a very low probability of adoption for small innovation performance with respect to the status quo and are especially sensitive to changes in the rate of learning and social pressure. However, they present an remarkable advantage in the time needed to achieve favorable consensus as compared with a hierarchical graph.The modelLet I = 1, 2, . . ., N be the set of nodes in a social system structure: each node represents an individual or a team of several individuals under a common working method (whether subject to discipline or reached by consensus). For each node j 2 I there is, at least, another node i 2 I,i 6?j to which it is connected; the graph of relationships is specified by a (N ?N) symmetric adjacency matrix A defined as Aij = 1 whenever i is directly connected to j in the social structure, or Aij = 0 otherwise. We define the influence set of node j as the collection of nodes that are directly connected to it: Hj = i 2 IjAij = 1. In the same way, the degree kj of node j is the number of PN nodes directly connected to it: kj ?card j ??i? Aij . Each node i 2 I has knowledge of each working method. Let Rit be the performance of node i at time t provided by the conventional method (status quo) and, in the same way, let R be t the node i's performance provided by the new method (innovation). In addition, each node i is characterized by a variable si (the strategy) that takes the value sit ?1 if the node i supports the innovation at time t, or sit ?0 otherwise. Let ait be the number of nodes connected to i that support the innovation at time t, and let bit be the number of i's neighbors that support the status quo: ait ?N X j? N X j?sjt Aij : ??j1 ?sjt jAij ?ki ?aitbit?Given two nodes (i, j) mutually connected, i having adopted the innovation and j having not (i.e., sit ?1; sjt ?0), we establish that they can interact with each other by exchanging knowledge (and exchanging methods) only if the performance difference between the two nodes is contained in an interval : j R ?Rjt j< ; t ??resulting in mutual learning. When condition 2 is satisfied, we define the link (i, j) as feasible. This threshold introduces a condition for mutual benefit: while high values of allow altruism (i.e., people with high performance help people with very low performance without expecting anything in return), low values of only allow win-win relationships.PLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,3 /The Role of the Organization Structure in the Diffusion of InnovationsInitial conditionsThe system begins with a number of randomly distributed nodes (the initial adopters) that adopt the innovation from the first moment t = 0, while the other nodes are supporters of the status quo. The performance provided by the status quo is randomly distributed between the nodes according to a gaussian distribution centered in R = 1 with.
